| Summary: | The research presented in this paper deals with analytic <i>p</i>-valent functions related to the generalized probability distribution in the open unit disk <i>U</i>. Using the Hadamard product or convolution, function <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mi>s</mi></msub><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> is defined as involving an analytic <i>p</i>-valent function and generalized distribution expressed in terms of analytic <i>p</i>-valent functions. Neighborhood properties for functions <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mi>s</mi></msub><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> are established. Further, by applying a previously introduced linear transformation to <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mi>s</mi></msub><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> and using an extended Libera integral operator, a new generalized Libera-type operator is defined. Moreover, using the same linear transformation, subclasses of starlike, convex, close-to-convex and spiralike functions are defined and investigated in order to obtain geometrical properties that characterize the new generalized Libera-type operator. Symmetry properties are due to the involvement of the Libera integral operator and convolution transform.
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